Properties

Label 289.10.a.g.1.34
Level $289$
Weight $10$
Character 289.1
Self dual yes
Analytic conductor $148.845$
Analytic rank $1$
Dimension $36$
CM no
Inner twists $1$

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Newspace parameters

Level: \( N \) \(=\) \( 289 = 17^{2} \)
Weight: \( k \) \(=\) \( 10 \)
Character orbit: \([\chi]\) \(=\) 289.a (trivial)

Newform invariants

Self dual: yes
Analytic conductor: \(148.845356651\)
Analytic rank: \(1\)
Dimension: \(36\)
Twist minimal: yes
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.34
Character \(\chi\) \(=\) 289.1

$q$-expansion

\(f(q)\) \(=\) \(q+39.9305 q^{2} -192.155 q^{3} +1082.44 q^{4} +2270.02 q^{5} -7672.86 q^{6} -10525.4 q^{7} +22778.2 q^{8} +17240.7 q^{9} +O(q^{10})\) \(q+39.9305 q^{2} -192.155 q^{3} +1082.44 q^{4} +2270.02 q^{5} -7672.86 q^{6} -10525.4 q^{7} +22778.2 q^{8} +17240.7 q^{9} +90643.1 q^{10} -26182.4 q^{11} -207998. q^{12} +130709. q^{13} -420285. q^{14} -436197. q^{15} +355331. q^{16} +688429. q^{18} -446045. q^{19} +2.45717e6 q^{20} +2.02251e6 q^{21} -1.04548e6 q^{22} +340450. q^{23} -4.37694e6 q^{24} +3.19988e6 q^{25} +5.21927e6 q^{26} +469307. q^{27} -1.13932e7 q^{28} -3.01654e6 q^{29} -1.74176e7 q^{30} -1.67993e6 q^{31} +2.52614e6 q^{32} +5.03109e6 q^{33} -2.38929e7 q^{35} +1.86621e7 q^{36} -1.57112e7 q^{37} -1.78108e7 q^{38} -2.51164e7 q^{39} +5.17069e7 q^{40} -1.68228e7 q^{41} +8.07600e7 q^{42} -4.62151e6 q^{43} -2.83410e7 q^{44} +3.91367e7 q^{45} +1.35943e7 q^{46} -5.82190e6 q^{47} -6.82788e7 q^{48} +7.04308e7 q^{49} +1.27773e8 q^{50} +1.41485e8 q^{52} +2.06125e7 q^{53} +1.87397e7 q^{54} -5.94347e7 q^{55} -2.39750e8 q^{56} +8.57099e7 q^{57} -1.20452e8 q^{58} -5.56955e7 q^{59} -4.72159e8 q^{60} +1.23184e8 q^{61} -6.70805e7 q^{62} -1.81465e8 q^{63} -8.10595e7 q^{64} +2.96712e8 q^{65} +2.00894e8 q^{66} -1.03447e8 q^{67} -6.54193e7 q^{69} -9.54057e8 q^{70} -2.91931e8 q^{71} +3.92711e8 q^{72} -2.25028e8 q^{73} -6.27356e8 q^{74} -6.14874e8 q^{75} -4.82819e8 q^{76} +2.75581e8 q^{77} -1.00291e9 q^{78} +6.19743e8 q^{79} +8.06610e8 q^{80} -4.29528e8 q^{81} -6.71744e8 q^{82} +1.60147e8 q^{83} +2.18926e9 q^{84} -1.84539e8 q^{86} +5.79644e8 q^{87} -5.96387e8 q^{88} +6.09272e8 q^{89} +1.56275e9 q^{90} -1.37576e9 q^{91} +3.68519e8 q^{92} +3.22808e8 q^{93} -2.32472e8 q^{94} -1.01253e9 q^{95} -4.85411e8 q^{96} -5.75873e8 q^{97} +2.81234e9 q^{98} -4.51403e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} + O(q^{10}) \) \( 36q - 486q^{3} + 9216q^{4} - 3750q^{5} - 11061q^{6} - 29040q^{7} + 24837q^{8} + 236196q^{9} - 60000q^{10} - 76902q^{11} - 373248q^{12} + 54216q^{13} - 17373q^{14} - 34122q^{15} + 2359296q^{16} - 1779435q^{18} - 245058q^{19} - 6439479q^{20} - 138102q^{21} - 267324q^{22} - 4041462q^{23} - 7653888q^{24} + 16582356q^{25} + 15822744q^{26} - 13281612q^{27} - 18614784q^{28} - 4005936q^{29} + 22471686q^{30} - 21257064q^{31} - 30922641q^{32} + 35736474q^{33} - 9039642q^{35} + 39076761q^{36} - 22076682q^{37} - 27401376q^{38} - 62736162q^{39} + 12231630q^{40} - 59641782q^{41} + 150001536q^{42} - 47951586q^{43} + 49578936q^{44} - 129308238q^{45} - 140524827q^{46} - 118557912q^{47} - 407719119q^{48} + 99849138q^{49} + 435669051q^{50} - 105017607q^{52} + 13698846q^{53} - 209848575q^{54} - 365439924q^{55} - 203095059q^{56} + 4614108q^{57} + 179071413q^{58} + 343015128q^{59} + 427179186q^{60} - 175597116q^{61} - 720602571q^{62} - 587415936q^{63} + 853082511q^{64} - 393820182q^{65} - 494661978q^{66} + 502776528q^{67} - 469106598q^{69} - 1062525966q^{70} - 1308709542q^{71} - 275337849q^{72} - 494841342q^{73} - 1545361890q^{74} - 1824677616q^{75} + 242064891q^{76} - 792768144q^{77} - 2270624538q^{78} - 1980107868q^{79} - 2897000199q^{80} + 1598298840q^{81} - 898743654q^{82} + 275294520q^{83} - 2144532369q^{84} - 2880848046q^{86} + 1088458710q^{87} + 2705904618q^{88} + 148394658q^{89} - 117916215q^{90} - 636340896q^{91} + 3458472327q^{92} - 628345524q^{93} - 200245965q^{94} - 4878626298q^{95} + 8390096634q^{96} + 891786822q^{97} + 4285627647q^{98} + 1476187998q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 39.9305 1.76470 0.882348 0.470598i \(-0.155962\pi\)
0.882348 + 0.470598i \(0.155962\pi\)
\(3\) −192.155 −1.36964 −0.684821 0.728712i \(-0.740119\pi\)
−0.684821 + 0.728712i \(0.740119\pi\)
\(4\) 1082.44 2.11415
\(5\) 2270.02 1.62430 0.812148 0.583451i \(-0.198298\pi\)
0.812148 + 0.583451i \(0.198298\pi\)
\(6\) −7672.86 −2.41700
\(7\) −10525.4 −1.65691 −0.828453 0.560058i \(-0.810779\pi\)
−0.828453 + 0.560058i \(0.810779\pi\)
\(8\) 22778.2 1.96614
\(9\) 17240.7 0.875917
\(10\) 90643.1 2.86639
\(11\) −26182.4 −0.539191 −0.269596 0.962974i \(-0.586890\pi\)
−0.269596 + 0.962974i \(0.586890\pi\)
\(12\) −207998. −2.89563
\(13\) 130709. 1.26929 0.634643 0.772805i \(-0.281147\pi\)
0.634643 + 0.772805i \(0.281147\pi\)
\(14\) −420285. −2.92394
\(15\) −436197. −2.22470
\(16\) 355331. 1.35548
\(17\) 0 0
\(18\) 688429. 1.54573
\(19\) −446045. −0.785213 −0.392607 0.919707i \(-0.628427\pi\)
−0.392607 + 0.919707i \(0.628427\pi\)
\(20\) 2.45717e6 3.43401
\(21\) 2.02251e6 2.26937
\(22\) −1.04548e6 −0.951509
\(23\) 340450. 0.253675 0.126838 0.991923i \(-0.459517\pi\)
0.126838 + 0.991923i \(0.459517\pi\)
\(24\) −4.37694e6 −2.69290
\(25\) 3.19988e6 1.63834
\(26\) 5.21927e6 2.23990
\(27\) 469307. 0.169949
\(28\) −1.13932e7 −3.50295
\(29\) −3.01654e6 −0.791986 −0.395993 0.918253i \(-0.629600\pi\)
−0.395993 + 0.918253i \(0.629600\pi\)
\(30\) −1.74176e7 −3.92592
\(31\) −1.67993e6 −0.326711 −0.163355 0.986567i \(-0.552232\pi\)
−0.163355 + 0.986567i \(0.552232\pi\)
\(32\) 2.52614e6 0.425876
\(33\) 5.03109e6 0.738499
\(34\) 0 0
\(35\) −2.38929e7 −2.69131
\(36\) 1.86621e7 1.85182
\(37\) −1.57112e7 −1.37817 −0.689083 0.724683i \(-0.741986\pi\)
−0.689083 + 0.724683i \(0.741986\pi\)
\(38\) −1.78108e7 −1.38566
\(39\) −2.51164e7 −1.73847
\(40\) 5.17069e7 3.19359
\(41\) −1.68228e7 −0.929762 −0.464881 0.885373i \(-0.653903\pi\)
−0.464881 + 0.885373i \(0.653903\pi\)
\(42\) 8.07600e7 4.00474
\(43\) −4.62151e6 −0.206146 −0.103073 0.994674i \(-0.532868\pi\)
−0.103073 + 0.994674i \(0.532868\pi\)
\(44\) −2.83410e7 −1.13993
\(45\) 3.91367e7 1.42275
\(46\) 1.35943e7 0.447660
\(47\) −5.82190e6 −0.174030 −0.0870151 0.996207i \(-0.527733\pi\)
−0.0870151 + 0.996207i \(0.527733\pi\)
\(48\) −6.82788e7 −1.85652
\(49\) 7.04308e7 1.74534
\(50\) 1.27773e8 2.89117
\(51\) 0 0
\(52\) 1.41485e8 2.68346
\(53\) 2.06125e7 0.358831 0.179416 0.983773i \(-0.442579\pi\)
0.179416 + 0.983773i \(0.442579\pi\)
\(54\) 1.87397e7 0.299909
\(55\) −5.94347e7 −0.875806
\(56\) −2.39750e8 −3.25770
\(57\) 8.57099e7 1.07546
\(58\) −1.20452e8 −1.39761
\(59\) −5.56955e7 −0.598393 −0.299196 0.954192i \(-0.596719\pi\)
−0.299196 + 0.954192i \(0.596719\pi\)
\(60\) −4.72159e8 −4.70336
\(61\) 1.23184e8 1.13912 0.569562 0.821949i \(-0.307113\pi\)
0.569562 + 0.821949i \(0.307113\pi\)
\(62\) −6.70805e7 −0.576545
\(63\) −1.81465e8 −1.45131
\(64\) −8.10595e7 −0.603940
\(65\) 2.96712e8 2.06170
\(66\) 2.00894e8 1.30323
\(67\) −1.03447e8 −0.627166 −0.313583 0.949561i \(-0.601529\pi\)
−0.313583 + 0.949561i \(0.601529\pi\)
\(68\) 0 0
\(69\) −6.54193e7 −0.347444
\(70\) −9.54057e8 −4.74934
\(71\) −2.91931e8 −1.36338 −0.681691 0.731640i \(-0.738755\pi\)
−0.681691 + 0.731640i \(0.738755\pi\)
\(72\) 3.92711e8 1.72217
\(73\) −2.25028e8 −0.927436 −0.463718 0.885983i \(-0.653485\pi\)
−0.463718 + 0.885983i \(0.653485\pi\)
\(74\) −6.27356e8 −2.43204
\(75\) −6.14874e8 −2.24393
\(76\) −4.82819e8 −1.66006
\(77\) 2.75581e8 0.893390
\(78\) −1.00291e9 −3.06786
\(79\) 6.19743e8 1.79015 0.895075 0.445915i \(-0.147122\pi\)
0.895075 + 0.445915i \(0.147122\pi\)
\(80\) 8.06610e8 2.20170
\(81\) −4.29528e8 −1.10869
\(82\) −6.71744e8 −1.64075
\(83\) 1.60147e8 0.370398 0.185199 0.982701i \(-0.440707\pi\)
0.185199 + 0.982701i \(0.440707\pi\)
\(84\) 2.18926e9 4.79778
\(85\) 0 0
\(86\) −1.84539e8 −0.363786
\(87\) 5.79644e8 1.08474
\(88\) −5.96387e8 −1.06012
\(89\) 6.09272e8 1.02933 0.514667 0.857390i \(-0.327915\pi\)
0.514667 + 0.857390i \(0.327915\pi\)
\(90\) 1.56275e9 2.51072
\(91\) −1.37576e9 −2.10309
\(92\) 3.68519e8 0.536308
\(93\) 3.22808e8 0.447477
\(94\) −2.32472e8 −0.307110
\(95\) −1.01253e9 −1.27542
\(96\) −4.85411e8 −0.583297
\(97\) −5.75873e8 −0.660471 −0.330236 0.943899i \(-0.607128\pi\)
−0.330236 + 0.943899i \(0.607128\pi\)
\(98\) 2.81234e9 3.07999
\(99\) −4.51403e8 −0.472287
\(100\) 3.46369e9 3.46369
\(101\) −8.22534e8 −0.786516 −0.393258 0.919428i \(-0.628652\pi\)
−0.393258 + 0.919428i \(0.628652\pi\)
\(102\) 0 0
\(103\) −7.21303e8 −0.631466 −0.315733 0.948848i \(-0.602250\pi\)
−0.315733 + 0.948848i \(0.602250\pi\)
\(104\) 2.97730e9 2.49559
\(105\) 4.59115e9 3.68613
\(106\) 8.23069e8 0.633228
\(107\) −2.46308e9 −1.81657 −0.908283 0.418357i \(-0.862606\pi\)
−0.908283 + 0.418357i \(0.862606\pi\)
\(108\) 5.07999e8 0.359299
\(109\) 2.68309e8 0.182061 0.0910304 0.995848i \(-0.470984\pi\)
0.0910304 + 0.995848i \(0.470984\pi\)
\(110\) −2.37326e9 −1.54553
\(111\) 3.01899e9 1.88759
\(112\) −3.74001e9 −2.24591
\(113\) −2.59778e9 −1.49882 −0.749409 0.662107i \(-0.769662\pi\)
−0.749409 + 0.662107i \(0.769662\pi\)
\(114\) 3.42244e9 1.89786
\(115\) 7.72830e8 0.412044
\(116\) −3.26524e9 −1.67438
\(117\) 2.25351e9 1.11179
\(118\) −2.22395e9 −1.05598
\(119\) 0 0
\(120\) −9.93576e9 −4.37407
\(121\) −1.67243e9 −0.709273
\(122\) 4.91881e9 2.01021
\(123\) 3.23260e9 1.27344
\(124\) −1.81843e9 −0.690716
\(125\) 2.83016e9 1.03685
\(126\) −7.24600e9 −2.56112
\(127\) −2.80736e9 −0.957595 −0.478797 0.877925i \(-0.658927\pi\)
−0.478797 + 0.877925i \(0.658927\pi\)
\(128\) −4.53013e9 −1.49165
\(129\) 8.88047e8 0.282347
\(130\) 1.18479e10 3.63827
\(131\) −4.93021e9 −1.46266 −0.731332 0.682022i \(-0.761101\pi\)
−0.731332 + 0.682022i \(0.761101\pi\)
\(132\) 5.44588e9 1.56130
\(133\) 4.69481e9 1.30103
\(134\) −4.13070e9 −1.10676
\(135\) 1.06534e9 0.276048
\(136\) 0 0
\(137\) −6.50097e9 −1.57665 −0.788325 0.615259i \(-0.789051\pi\)
−0.788325 + 0.615259i \(0.789051\pi\)
\(138\) −2.61223e9 −0.613133
\(139\) 6.50760e9 1.47861 0.739306 0.673370i \(-0.235154\pi\)
0.739306 + 0.673370i \(0.235154\pi\)
\(140\) −2.58628e10 −5.68983
\(141\) 1.11871e9 0.238359
\(142\) −1.16569e10 −2.40595
\(143\) −3.42227e9 −0.684388
\(144\) 6.12615e9 1.18729
\(145\) −6.84761e9 −1.28642
\(146\) −8.98548e9 −1.63664
\(147\) −1.35336e10 −2.39049
\(148\) −1.70065e10 −2.91365
\(149\) −5.06101e9 −0.841199 −0.420600 0.907246i \(-0.638180\pi\)
−0.420600 + 0.907246i \(0.638180\pi\)
\(150\) −2.45522e10 −3.95986
\(151\) −1.65176e9 −0.258553 −0.129277 0.991609i \(-0.541266\pi\)
−0.129277 + 0.991609i \(0.541266\pi\)
\(152\) −1.01601e10 −1.54384
\(153\) 0 0
\(154\) 1.10041e10 1.57656
\(155\) −3.81348e9 −0.530675
\(156\) −2.71871e10 −3.67538
\(157\) 1.14123e10 1.49908 0.749542 0.661957i \(-0.230274\pi\)
0.749542 + 0.661957i \(0.230274\pi\)
\(158\) 2.47466e10 3.15907
\(159\) −3.96081e9 −0.491470
\(160\) 5.73440e9 0.691748
\(161\) −3.58338e9 −0.420317
\(162\) −1.71513e10 −1.95649
\(163\) 6.03422e9 0.669541 0.334770 0.942300i \(-0.391341\pi\)
0.334770 + 0.942300i \(0.391341\pi\)
\(164\) −1.82098e10 −1.96566
\(165\) 1.14207e10 1.19954
\(166\) 6.39476e9 0.653639
\(167\) 9.15503e8 0.0910827 0.0455413 0.998962i \(-0.485499\pi\)
0.0455413 + 0.998962i \(0.485499\pi\)
\(168\) 4.60692e10 4.46189
\(169\) 6.48028e9 0.611088
\(170\) 0 0
\(171\) −7.69012e9 −0.687781
\(172\) −5.00253e9 −0.435824
\(173\) −1.14509e10 −0.971920 −0.485960 0.873981i \(-0.661530\pi\)
−0.485960 + 0.873981i \(0.661530\pi\)
\(174\) 2.31455e10 1.91423
\(175\) −3.36801e10 −2.71457
\(176\) −9.30344e9 −0.730864
\(177\) 1.07022e10 0.819583
\(178\) 2.43286e10 1.81646
\(179\) −8.16576e9 −0.594508 −0.297254 0.954798i \(-0.596071\pi\)
−0.297254 + 0.954798i \(0.596071\pi\)
\(180\) 4.23633e10 3.00790
\(181\) 1.94229e10 1.34512 0.672561 0.740042i \(-0.265194\pi\)
0.672561 + 0.740042i \(0.265194\pi\)
\(182\) −5.49349e10 −3.71131
\(183\) −2.36705e10 −1.56019
\(184\) 7.75483e9 0.498760
\(185\) −3.56648e10 −2.23855
\(186\) 1.28899e10 0.789660
\(187\) 0 0
\(188\) −6.30189e9 −0.367926
\(189\) −4.93965e9 −0.281590
\(190\) −4.04309e10 −2.25073
\(191\) −2.56201e10 −1.39293 −0.696467 0.717588i \(-0.745246\pi\)
−0.696467 + 0.717588i \(0.745246\pi\)
\(192\) 1.55760e10 0.827182
\(193\) 3.24728e10 1.68466 0.842329 0.538963i \(-0.181184\pi\)
0.842329 + 0.538963i \(0.181184\pi\)
\(194\) −2.29949e10 −1.16553
\(195\) −5.70148e10 −2.82378
\(196\) 7.62374e10 3.68991
\(197\) 3.93713e10 1.86244 0.931219 0.364461i \(-0.118747\pi\)
0.931219 + 0.364461i \(0.118747\pi\)
\(198\) −1.80247e10 −0.833442
\(199\) −2.57185e9 −0.116254 −0.0581268 0.998309i \(-0.518513\pi\)
−0.0581268 + 0.998309i \(0.518513\pi\)
\(200\) 7.28873e10 3.22119
\(201\) 1.98779e10 0.858992
\(202\) −3.28442e10 −1.38796
\(203\) 3.17503e10 1.31225
\(204\) 0 0
\(205\) −3.81882e10 −1.51021
\(206\) −2.88020e10 −1.11435
\(207\) 5.86959e9 0.222199
\(208\) 4.64449e10 1.72049
\(209\) 1.16785e10 0.423380
\(210\) 1.83327e11 6.50489
\(211\) 1.81456e10 0.630231 0.315116 0.949053i \(-0.397957\pi\)
0.315116 + 0.949053i \(0.397957\pi\)
\(212\) 2.23120e10 0.758623
\(213\) 5.60961e10 1.86734
\(214\) −9.83519e10 −3.20569
\(215\) −1.04909e10 −0.334843
\(216\) 1.06899e10 0.334144
\(217\) 1.76820e10 0.541330
\(218\) 1.07137e10 0.321282
\(219\) 4.32403e10 1.27025
\(220\) −6.43348e10 −1.85159
\(221\) 0 0
\(222\) 1.20550e11 3.33103
\(223\) −1.42142e10 −0.384903 −0.192451 0.981307i \(-0.561644\pi\)
−0.192451 + 0.981307i \(0.561644\pi\)
\(224\) −2.65887e10 −0.705636
\(225\) 5.51680e10 1.43505
\(226\) −1.03731e11 −2.64496
\(227\) −7.38003e10 −1.84477 −0.922384 0.386274i \(-0.873762\pi\)
−0.922384 + 0.386274i \(0.873762\pi\)
\(228\) 9.27763e10 2.27368
\(229\) 1.62402e10 0.390240 0.195120 0.980779i \(-0.437490\pi\)
0.195120 + 0.980779i \(0.437490\pi\)
\(230\) 3.08595e10 0.727132
\(231\) −5.29544e10 −1.22362
\(232\) −6.87112e10 −1.55715
\(233\) 1.91917e10 0.426590 0.213295 0.976988i \(-0.431580\pi\)
0.213295 + 0.976988i \(0.431580\pi\)
\(234\) 8.99836e10 1.96197
\(235\) −1.32159e10 −0.282677
\(236\) −6.02874e10 −1.26509
\(237\) −1.19087e11 −2.45186
\(238\) 0 0
\(239\) 2.13762e10 0.423780 0.211890 0.977294i \(-0.432038\pi\)
0.211890 + 0.977294i \(0.432038\pi\)
\(240\) −1.54994e11 −3.01554
\(241\) −6.20535e10 −1.18492 −0.592461 0.805599i \(-0.701844\pi\)
−0.592461 + 0.805599i \(0.701844\pi\)
\(242\) −6.67809e10 −1.25165
\(243\) 7.32987e10 1.34855
\(244\) 1.33340e11 2.40828
\(245\) 1.59879e11 2.83495
\(246\) 1.29079e11 2.24723
\(247\) −5.83020e10 −0.996660
\(248\) −3.82657e10 −0.642358
\(249\) −3.07732e10 −0.507312
\(250\) 1.13010e11 1.82972
\(251\) −5.99268e10 −0.952992 −0.476496 0.879177i \(-0.658093\pi\)
−0.476496 + 0.879177i \(0.658093\pi\)
\(252\) −1.96426e11 −3.06829
\(253\) −8.91382e9 −0.136780
\(254\) −1.12099e11 −1.68986
\(255\) 0 0
\(256\) −1.39388e11 −2.02836
\(257\) 1.24917e10 0.178616 0.0893081 0.996004i \(-0.471534\pi\)
0.0893081 + 0.996004i \(0.471534\pi\)
\(258\) 3.54602e10 0.498256
\(259\) 1.65367e11 2.28349
\(260\) 3.21174e11 4.35874
\(261\) −5.20071e10 −0.693714
\(262\) −1.96866e11 −2.58116
\(263\) 5.97877e10 0.770569 0.385284 0.922798i \(-0.374103\pi\)
0.385284 + 0.922798i \(0.374103\pi\)
\(264\) 1.14599e11 1.45199
\(265\) 4.67910e10 0.582848
\(266\) 1.87466e11 2.29591
\(267\) −1.17075e11 −1.40982
\(268\) −1.11976e11 −1.32592
\(269\) 4.76191e10 0.554493 0.277246 0.960799i \(-0.410578\pi\)
0.277246 + 0.960799i \(0.410578\pi\)
\(270\) 4.25394e10 0.487141
\(271\) 2.21456e10 0.249417 0.124709 0.992193i \(-0.460200\pi\)
0.124709 + 0.992193i \(0.460200\pi\)
\(272\) 0 0
\(273\) 2.64360e11 2.88048
\(274\) −2.59587e11 −2.78231
\(275\) −8.37806e10 −0.883378
\(276\) −7.08128e10 −0.734549
\(277\) 9.60150e10 0.979896 0.489948 0.871752i \(-0.337016\pi\)
0.489948 + 0.871752i \(0.337016\pi\)
\(278\) 2.59852e11 2.60930
\(279\) −2.89631e10 −0.286172
\(280\) −5.44237e11 −5.29148
\(281\) 5.47493e10 0.523842 0.261921 0.965089i \(-0.415644\pi\)
0.261921 + 0.965089i \(0.415644\pi\)
\(282\) 4.46707e10 0.420631
\(283\) 1.95278e11 1.80973 0.904865 0.425699i \(-0.139972\pi\)
0.904865 + 0.425699i \(0.139972\pi\)
\(284\) −3.15999e11 −2.88239
\(285\) 1.94564e11 1.74687
\(286\) −1.36653e11 −1.20774
\(287\) 1.77067e11 1.54053
\(288\) 4.35524e10 0.373032
\(289\) 0 0
\(290\) −2.73428e11 −2.27014
\(291\) 1.10657e11 0.904608
\(292\) −2.43580e11 −1.96074
\(293\) −7.82174e10 −0.620010 −0.310005 0.950735i \(-0.600331\pi\)
−0.310005 + 0.950735i \(0.600331\pi\)
\(294\) −5.40405e11 −4.21849
\(295\) −1.26430e11 −0.971967
\(296\) −3.57872e11 −2.70966
\(297\) −1.22876e10 −0.0916353
\(298\) −2.02089e11 −1.48446
\(299\) 4.44998e10 0.321987
\(300\) −6.65567e11 −4.74402
\(301\) 4.86433e10 0.341565
\(302\) −6.59555e10 −0.456268
\(303\) 1.58054e11 1.07724
\(304\) −1.58494e11 −1.06434
\(305\) 2.79631e11 1.85027
\(306\) 0 0
\(307\) −1.90235e11 −1.22227 −0.611136 0.791526i \(-0.709287\pi\)
−0.611136 + 0.791526i \(0.709287\pi\)
\(308\) 2.98301e11 1.88876
\(309\) 1.38602e11 0.864882
\(310\) −1.52274e11 −0.936480
\(311\) 8.33297e10 0.505101 0.252550 0.967584i \(-0.418731\pi\)
0.252550 + 0.967584i \(0.418731\pi\)
\(312\) −5.72105e11 −3.41806
\(313\) 2.01585e11 1.18716 0.593580 0.804775i \(-0.297714\pi\)
0.593580 + 0.804775i \(0.297714\pi\)
\(314\) 4.55700e11 2.64543
\(315\) −4.11930e11 −2.35736
\(316\) 6.70838e11 3.78465
\(317\) 1.02689e10 0.0571158 0.0285579 0.999592i \(-0.490909\pi\)
0.0285579 + 0.999592i \(0.490909\pi\)
\(318\) −1.58157e11 −0.867295
\(319\) 7.89803e10 0.427032
\(320\) −1.84007e11 −0.980978
\(321\) 4.73294e11 2.48804
\(322\) −1.43086e11 −0.741731
\(323\) 0 0
\(324\) −4.64940e11 −2.34393
\(325\) 4.18252e11 2.07952
\(326\) 2.40949e11 1.18154
\(327\) −5.15571e10 −0.249358
\(328\) −3.83193e11 −1.82804
\(329\) 6.12780e10 0.288352
\(330\) 4.56034e11 2.11682
\(331\) 4.20342e10 0.192476 0.0962380 0.995358i \(-0.469319\pi\)
0.0962380 + 0.995358i \(0.469319\pi\)
\(332\) 1.73351e11 0.783076
\(333\) −2.70871e11 −1.20716
\(334\) 3.65565e10 0.160733
\(335\) −2.34828e11 −1.01870
\(336\) 7.18663e11 3.07609
\(337\) 1.17165e11 0.494840 0.247420 0.968908i \(-0.420417\pi\)
0.247420 + 0.968908i \(0.420417\pi\)
\(338\) 2.58761e11 1.07838
\(339\) 4.99177e11 2.05284
\(340\) 0 0
\(341\) 4.39847e10 0.176160
\(342\) −3.07070e11 −1.21372
\(343\) −3.16575e11 −1.23496
\(344\) −1.05269e11 −0.405312
\(345\) −1.48503e11 −0.564352
\(346\) −4.57239e11 −1.71514
\(347\) −8.63930e10 −0.319886 −0.159943 0.987126i \(-0.551131\pi\)
−0.159943 + 0.987126i \(0.551131\pi\)
\(348\) 6.27432e11 2.29330
\(349\) 7.38933e10 0.266619 0.133309 0.991074i \(-0.457440\pi\)
0.133309 + 0.991074i \(0.457440\pi\)
\(350\) −1.34486e12 −4.79040
\(351\) 6.13425e10 0.215715
\(352\) −6.61405e10 −0.229628
\(353\) 5.59145e10 0.191663 0.0958315 0.995398i \(-0.469449\pi\)
0.0958315 + 0.995398i \(0.469449\pi\)
\(354\) 4.27344e11 1.44632
\(355\) −6.62690e11 −2.21454
\(356\) 6.59504e11 2.17617
\(357\) 0 0
\(358\) −3.26063e11 −1.04913
\(359\) 1.53879e11 0.488937 0.244469 0.969657i \(-0.421387\pi\)
0.244469 + 0.969657i \(0.421387\pi\)
\(360\) 8.91462e11 2.79732
\(361\) −1.23731e11 −0.383440
\(362\) 7.75568e11 2.37373
\(363\) 3.21366e11 0.971449
\(364\) −1.48919e12 −4.44625
\(365\) −5.10819e11 −1.50643
\(366\) −9.45175e11 −2.75326
\(367\) −2.65608e11 −0.764265 −0.382132 0.924108i \(-0.624810\pi\)
−0.382132 + 0.924108i \(0.624810\pi\)
\(368\) 1.20973e11 0.343852
\(369\) −2.90037e11 −0.814394
\(370\) −1.42411e12 −3.95036
\(371\) −2.16956e11 −0.594550
\(372\) 3.49421e11 0.946033
\(373\) −1.61393e11 −0.431713 −0.215857 0.976425i \(-0.569254\pi\)
−0.215857 + 0.976425i \(0.569254\pi\)
\(374\) 0 0
\(375\) −5.43830e11 −1.42011
\(376\) −1.32612e11 −0.342167
\(377\) −3.94288e11 −1.00526
\(378\) −1.97243e11 −0.496921
\(379\) 1.58023e11 0.393408 0.196704 0.980463i \(-0.436976\pi\)
0.196704 + 0.980463i \(0.436976\pi\)
\(380\) −1.09601e12 −2.69643
\(381\) 5.39450e11 1.31156
\(382\) −1.02302e12 −2.45811
\(383\) 4.20992e11 0.999722 0.499861 0.866106i \(-0.333384\pi\)
0.499861 + 0.866106i \(0.333384\pi\)
\(384\) 8.70489e11 2.04302
\(385\) 6.25575e11 1.45113
\(386\) 1.29666e12 2.97291
\(387\) −7.96779e10 −0.180567
\(388\) −6.23351e11 −1.39634
\(389\) −5.78199e11 −1.28028 −0.640139 0.768259i \(-0.721123\pi\)
−0.640139 + 0.768259i \(0.721123\pi\)
\(390\) −2.27663e12 −4.98312
\(391\) 0 0
\(392\) 1.60428e12 3.43158
\(393\) 9.47366e11 2.00332
\(394\) 1.57212e12 3.28663
\(395\) 1.40683e12 2.90773
\(396\) −4.88619e11 −0.998485
\(397\) 6.39613e11 1.29229 0.646145 0.763215i \(-0.276380\pi\)
0.646145 + 0.763215i \(0.276380\pi\)
\(398\) −1.02695e11 −0.205152
\(399\) −9.02133e11 −1.78194
\(400\) 1.13702e12 2.22074
\(401\) −5.74794e11 −1.11010 −0.555051 0.831816i \(-0.687301\pi\)
−0.555051 + 0.831816i \(0.687301\pi\)
\(402\) 7.93736e11 1.51586
\(403\) −2.19582e11 −0.414690
\(404\) −8.90347e11 −1.66281
\(405\) −9.75038e11 −1.80084
\(406\) 1.26781e12 2.31572
\(407\) 4.11357e11 0.743095
\(408\) 0 0
\(409\) −3.11632e11 −0.550664 −0.275332 0.961349i \(-0.588788\pi\)
−0.275332 + 0.961349i \(0.588788\pi\)
\(410\) −1.52487e12 −2.66506
\(411\) 1.24920e12 2.15944
\(412\) −7.80770e11 −1.33501
\(413\) 5.86219e11 0.991481
\(414\) 2.34376e11 0.392113
\(415\) 3.63538e11 0.601635
\(416\) 3.30189e11 0.540558
\(417\) −1.25047e12 −2.02517
\(418\) 4.66330e11 0.747137
\(419\) −2.81135e11 −0.445608 −0.222804 0.974863i \(-0.571521\pi\)
−0.222804 + 0.974863i \(0.571521\pi\)
\(420\) 4.96967e12 7.79302
\(421\) 1.12765e12 1.74947 0.874733 0.484605i \(-0.161037\pi\)
0.874733 + 0.484605i \(0.161037\pi\)
\(422\) 7.24562e11 1.11217
\(423\) −1.00374e11 −0.152436
\(424\) 4.69516e11 0.705511
\(425\) 0 0
\(426\) 2.23995e12 3.29529
\(427\) −1.29657e12 −1.88742
\(428\) −2.66615e12 −3.84049
\(429\) 6.57608e11 0.937366
\(430\) −4.18908e11 −0.590895
\(431\) 4.10369e10 0.0572831 0.0286416 0.999590i \(-0.490882\pi\)
0.0286416 + 0.999590i \(0.490882\pi\)
\(432\) 1.66759e11 0.230363
\(433\) 9.68299e11 1.32377 0.661887 0.749604i \(-0.269756\pi\)
0.661887 + 0.749604i \(0.269756\pi\)
\(434\) 7.06050e11 0.955282
\(435\) 1.31580e12 1.76193
\(436\) 2.90430e11 0.384904
\(437\) −1.51856e11 −0.199189
\(438\) 1.72661e12 2.24161
\(439\) 1.39595e12 1.79382 0.896912 0.442208i \(-0.145805\pi\)
0.896912 + 0.442208i \(0.145805\pi\)
\(440\) −1.35381e12 −1.72195
\(441\) 1.21427e12 1.52877
\(442\) 0 0
\(443\) 2.85808e11 0.352580 0.176290 0.984338i \(-0.443590\pi\)
0.176290 + 0.984338i \(0.443590\pi\)
\(444\) 3.26789e12 3.99065
\(445\) 1.38306e12 1.67194
\(446\) −5.67580e11 −0.679236
\(447\) 9.72500e11 1.15214
\(448\) 8.53185e11 1.00067
\(449\) 4.26432e11 0.495156 0.247578 0.968868i \(-0.420365\pi\)
0.247578 + 0.968868i \(0.420365\pi\)
\(450\) 2.20289e12 2.53242
\(451\) 4.40463e11 0.501320
\(452\) −2.81195e12 −3.16873
\(453\) 3.17394e11 0.354125
\(454\) −2.94688e12 −3.25545
\(455\) −3.12302e12 −3.41604
\(456\) 1.95231e12 2.11450
\(457\) 9.18833e11 0.985403 0.492701 0.870198i \(-0.336010\pi\)
0.492701 + 0.870198i \(0.336010\pi\)
\(458\) 6.48479e11 0.688654
\(459\) 0 0
\(460\) 8.36546e11 0.871123
\(461\) 1.32769e12 1.36912 0.684559 0.728957i \(-0.259995\pi\)
0.684559 + 0.728957i \(0.259995\pi\)
\(462\) −2.11449e12 −2.15932
\(463\) −2.36101e11 −0.238772 −0.119386 0.992848i \(-0.538093\pi\)
−0.119386 + 0.992848i \(0.538093\pi\)
\(464\) −1.07187e12 −1.07352
\(465\) 7.32781e11 0.726835
\(466\) 7.66333e11 0.752802
\(467\) 2.97347e11 0.289293 0.144647 0.989483i \(-0.453795\pi\)
0.144647 + 0.989483i \(0.453795\pi\)
\(468\) 2.43930e12 2.35049
\(469\) 1.08883e12 1.03916
\(470\) −5.27716e11 −0.498838
\(471\) −2.19294e12 −2.05321
\(472\) −1.26864e12 −1.17652
\(473\) 1.21002e11 0.111152
\(474\) −4.75520e12 −4.32679
\(475\) −1.42729e12 −1.28644
\(476\) 0 0
\(477\) 3.55374e11 0.314306
\(478\) 8.53563e11 0.747842
\(479\) 3.85863e11 0.334906 0.167453 0.985880i \(-0.446446\pi\)
0.167453 + 0.985880i \(0.446446\pi\)
\(480\) −1.10190e12 −0.947447
\(481\) −2.05359e12 −1.74929
\(482\) −2.47783e12 −2.09103
\(483\) 6.88566e11 0.575683
\(484\) −1.81031e12 −1.49951
\(485\) −1.30724e12 −1.07280
\(486\) 2.92685e12 2.37979
\(487\) 3.74600e11 0.301778 0.150889 0.988551i \(-0.451786\pi\)
0.150889 + 0.988551i \(0.451786\pi\)
\(488\) 2.80591e12 2.23967
\(489\) −1.15951e12 −0.917030
\(490\) 6.38407e12 5.00282
\(491\) −2.24428e12 −1.74265 −0.871324 0.490708i \(-0.836738\pi\)
−0.871324 + 0.490708i \(0.836738\pi\)
\(492\) 3.49911e12 2.69224
\(493\) 0 0
\(494\) −2.32803e12 −1.75880
\(495\) −1.02469e12 −0.767133
\(496\) −5.96932e11 −0.442851
\(497\) 3.07269e12 2.25900
\(498\) −1.22879e12 −0.895251
\(499\) 2.05931e12 1.48686 0.743429 0.668815i \(-0.233198\pi\)
0.743429 + 0.668815i \(0.233198\pi\)
\(500\) 3.06349e12 2.19206
\(501\) −1.75919e11 −0.124751
\(502\) −2.39291e12 −1.68174
\(503\) −6.76592e11 −0.471271 −0.235636 0.971841i \(-0.575717\pi\)
−0.235636 + 0.971841i \(0.575717\pi\)
\(504\) −4.13344e12 −2.85348
\(505\) −1.86717e12 −1.27753
\(506\) −3.55933e11 −0.241374
\(507\) −1.24522e12 −0.836971
\(508\) −3.03882e12 −2.02450
\(509\) −1.65744e12 −1.09448 −0.547240 0.836976i \(-0.684321\pi\)
−0.547240 + 0.836976i \(0.684321\pi\)
\(510\) 0 0
\(511\) 2.36851e12 1.53667
\(512\) −3.24640e12 −2.08779
\(513\) −2.09332e11 −0.133447
\(514\) 4.98798e11 0.315203
\(515\) −1.63737e12 −1.02569
\(516\) 9.61262e11 0.596923
\(517\) 1.52432e11 0.0938356
\(518\) 6.60318e12 4.02967
\(519\) 2.20034e12 1.33118
\(520\) 6.75855e12 4.05358
\(521\) −3.35020e11 −0.199205 −0.0996027 0.995027i \(-0.531757\pi\)
−0.0996027 + 0.995027i \(0.531757\pi\)
\(522\) −2.07667e12 −1.22419
\(523\) −1.54766e12 −0.904519 −0.452260 0.891886i \(-0.649382\pi\)
−0.452260 + 0.891886i \(0.649382\pi\)
\(524\) −5.33668e12 −3.09229
\(525\) 6.47180e12 3.71799
\(526\) 2.38735e12 1.35982
\(527\) 0 0
\(528\) 1.78770e12 1.00102
\(529\) −1.68525e12 −0.935649
\(530\) 1.86839e12 1.02855
\(531\) −9.60229e11 −0.524142
\(532\) 5.08187e12 2.75056
\(533\) −2.19889e12 −1.18013
\(534\) −4.67486e12 −2.48790
\(535\) −5.59124e12 −2.95064
\(536\) −2.35634e12 −1.23309
\(537\) 1.56909e12 0.814263
\(538\) 1.90145e12 0.978511
\(539\) −1.84405e12 −0.941072
\(540\) 1.15317e12 0.583607
\(541\) −1.39774e11 −0.0701518 −0.0350759 0.999385i \(-0.511167\pi\)
−0.0350759 + 0.999385i \(0.511167\pi\)
\(542\) 8.84287e11 0.440145
\(543\) −3.73222e12 −1.84233
\(544\) 0 0
\(545\) 6.09068e11 0.295721
\(546\) 1.05560e13 5.08317
\(547\) −2.71387e12 −1.29612 −0.648062 0.761587i \(-0.724420\pi\)
−0.648062 + 0.761587i \(0.724420\pi\)
\(548\) −7.03694e12 −3.33328
\(549\) 2.12378e12 0.997777
\(550\) −3.34540e12 −1.55889
\(551\) 1.34551e12 0.621878
\(552\) −1.49013e12 −0.683123
\(553\) −6.52305e12 −2.96611
\(554\) 3.83393e12 1.72922
\(555\) 6.85317e12 3.06601
\(556\) 7.04412e12 3.12601
\(557\) 1.13986e12 0.501769 0.250884 0.968017i \(-0.419279\pi\)
0.250884 + 0.968017i \(0.419279\pi\)
\(558\) −1.15651e12 −0.505006
\(559\) −6.04072e11 −0.261659
\(560\) −8.48991e12 −3.64802
\(561\) 0 0
\(562\) 2.18617e12 0.924421
\(563\) 1.30558e12 0.547667 0.273834 0.961777i \(-0.411708\pi\)
0.273834 + 0.961777i \(0.411708\pi\)
\(564\) 1.21094e12 0.503927
\(565\) −5.89701e12 −2.43452
\(566\) 7.79753e12 3.19362
\(567\) 4.52096e12 1.83699
\(568\) −6.64965e12 −2.68059
\(569\) 1.81208e12 0.724722 0.362361 0.932038i \(-0.381971\pi\)
0.362361 + 0.932038i \(0.381971\pi\)
\(570\) 7.76902e12 3.08269
\(571\) −5.00343e12 −1.96972 −0.984862 0.173340i \(-0.944544\pi\)
−0.984862 + 0.173340i \(0.944544\pi\)
\(572\) −3.70442e12 −1.44690
\(573\) 4.92304e12 1.90782
\(574\) 7.07039e12 2.71856
\(575\) 1.08940e12 0.415606
\(576\) −1.39752e12 −0.529002
\(577\) 2.87243e11 0.107884 0.0539422 0.998544i \(-0.482821\pi\)
0.0539422 + 0.998544i \(0.482821\pi\)
\(578\) 0 0
\(579\) −6.23982e12 −2.30738
\(580\) −7.41216e12 −2.71969
\(581\) −1.68562e12 −0.613714
\(582\) 4.41859e12 1.59636
\(583\) −5.39687e11 −0.193479
\(584\) −5.12572e12 −1.82346
\(585\) 5.11551e12 1.80587
\(586\) −3.12326e12 −1.09413
\(587\) 2.18972e12 0.761232 0.380616 0.924733i \(-0.375712\pi\)
0.380616 + 0.924733i \(0.375712\pi\)
\(588\) −1.46494e13 −5.05386
\(589\) 7.49325e11 0.256538
\(590\) −5.04842e12 −1.71523
\(591\) −7.56540e12 −2.55087
\(592\) −5.58268e12 −1.86808
\(593\) 7.91217e11 0.262754 0.131377 0.991332i \(-0.458060\pi\)
0.131377 + 0.991332i \(0.458060\pi\)
\(594\) −4.90650e11 −0.161708
\(595\) 0 0
\(596\) −5.47826e12 −1.77842
\(597\) 4.94194e11 0.159226
\(598\) 1.77690e12 0.568209
\(599\) 3.64233e12 1.15600 0.578001 0.816036i \(-0.303833\pi\)
0.578001 + 0.816036i \(0.303833\pi\)
\(600\) −1.40057e13 −4.41188
\(601\) −6.61320e11 −0.206765 −0.103382 0.994642i \(-0.532967\pi\)
−0.103382 + 0.994642i \(0.532967\pi\)
\(602\) 1.94235e12 0.602759
\(603\) −1.78350e12 −0.549345
\(604\) −1.78794e12 −0.546620
\(605\) −3.79645e12 −1.15207
\(606\) 6.31118e12 1.90101
\(607\) 6.37807e11 0.190695 0.0953477 0.995444i \(-0.469604\pi\)
0.0953477 + 0.995444i \(0.469604\pi\)
\(608\) −1.12677e12 −0.334403
\(609\) −6.10099e12 −1.79731
\(610\) 1.11658e13 3.26517
\(611\) −7.60974e11 −0.220894
\(612\) 0 0
\(613\) 4.20031e12 1.20146 0.600729 0.799452i \(-0.294877\pi\)
0.600729 + 0.799452i \(0.294877\pi\)
\(614\) −7.59618e12 −2.15694
\(615\) 7.33807e12 2.06844
\(616\) 6.27723e12 1.75653
\(617\) 5.36107e12 1.48925 0.744625 0.667483i \(-0.232628\pi\)
0.744625 + 0.667483i \(0.232628\pi\)
\(618\) 5.53445e12 1.52625
\(619\) 5.27140e10 0.0144317 0.00721586 0.999974i \(-0.497703\pi\)
0.00721586 + 0.999974i \(0.497703\pi\)
\(620\) −4.12788e12 −1.12193
\(621\) 1.59776e11 0.0431120
\(622\) 3.32740e12 0.891349
\(623\) −6.41285e12 −1.70551
\(624\) −8.92464e12 −2.35646
\(625\) 1.74762e11 0.0458129
\(626\) 8.04940e12 2.09498
\(627\) −2.24409e12 −0.579879
\(628\) 1.23532e13 3.16929
\(629\) 0 0
\(630\) −1.64486e13 −4.16002
\(631\) 4.08326e12 1.02536 0.512678 0.858581i \(-0.328653\pi\)
0.512678 + 0.858581i \(0.328653\pi\)
\(632\) 1.41166e13 3.51968
\(633\) −3.48677e12 −0.863191
\(634\) 4.10041e11 0.100792
\(635\) −6.37278e12 −1.55542
\(636\) −4.28736e12 −1.03904
\(637\) 9.20592e12 2.21534
\(638\) 3.15372e12 0.753582
\(639\) −5.03309e12 −1.19421
\(640\) −1.02835e13 −2.42288
\(641\) 1.09935e12 0.257203 0.128601 0.991696i \(-0.458951\pi\)
0.128601 + 0.991696i \(0.458951\pi\)
\(642\) 1.88988e13 4.39064
\(643\) −7.93048e12 −1.82957 −0.914787 0.403937i \(-0.867642\pi\)
−0.914787 + 0.403937i \(0.867642\pi\)
\(644\) −3.87881e12 −0.888612
\(645\) 2.01589e12 0.458614
\(646\) 0 0
\(647\) −5.70401e12 −1.27971 −0.639854 0.768496i \(-0.721005\pi\)
−0.639854 + 0.768496i \(0.721005\pi\)
\(648\) −9.78385e12 −2.17983
\(649\) 1.45824e12 0.322648
\(650\) 1.67010e13 3.66972
\(651\) −3.39768e12 −0.741427
\(652\) 6.53171e12 1.41551
\(653\) 1.03269e12 0.222260 0.111130 0.993806i \(-0.464553\pi\)
0.111130 + 0.993806i \(0.464553\pi\)
\(654\) −2.05870e12 −0.440041
\(655\) −1.11917e13 −2.37580
\(656\) −5.97768e12 −1.26027
\(657\) −3.87963e12 −0.812356
\(658\) 2.44686e12 0.508853
\(659\) 3.77448e12 0.779601 0.389801 0.920899i \(-0.372544\pi\)
0.389801 + 0.920899i \(0.372544\pi\)
\(660\) 1.23623e13 2.53601
\(661\) −6.49086e12 −1.32250 −0.661250 0.750166i \(-0.729974\pi\)
−0.661250 + 0.750166i \(0.729974\pi\)
\(662\) 1.67845e12 0.339662
\(663\) 0 0
\(664\) 3.64786e12 0.728252
\(665\) 1.06573e13 2.11325
\(666\) −1.08160e13 −2.13027
\(667\) −1.02698e12 −0.200907
\(668\) 9.90982e11 0.192562
\(669\) 2.73134e12 0.527178
\(670\) −9.37679e12 −1.79770
\(671\) −3.22526e12 −0.614206
\(672\) 5.10916e12 0.966468
\(673\) −3.32644e12 −0.625045 −0.312523 0.949910i \(-0.601174\pi\)
−0.312523 + 0.949910i \(0.601174\pi\)
\(674\) 4.67847e12 0.873242
\(675\) 1.50172e12 0.278435
\(676\) 7.01454e12 1.29193
\(677\) −7.88907e12 −1.44337 −0.721683 0.692224i \(-0.756631\pi\)
−0.721683 + 0.692224i \(0.756631\pi\)
\(678\) 1.99324e13 3.62264
\(679\) 6.06130e12 1.09434
\(680\) 0 0
\(681\) 1.41811e13 2.52667
\(682\) 1.75633e12 0.310868
\(683\) −5.91580e12 −1.04021 −0.520105 0.854103i \(-0.674107\pi\)
−0.520105 + 0.854103i \(0.674107\pi\)
\(684\) −8.32413e12 −1.45407
\(685\) −1.47573e13 −2.56095
\(686\) −1.26410e13 −2.17933
\(687\) −3.12064e12 −0.534488
\(688\) −1.64217e12 −0.279428
\(689\) 2.69424e12 0.455460
\(690\) −5.92981e12 −0.995910
\(691\) 5.47987e12 0.914363 0.457182 0.889373i \(-0.348859\pi\)
0.457182 + 0.889373i \(0.348859\pi\)
\(692\) −1.23949e13 −2.05479
\(693\) 4.75120e12 0.782535
\(694\) −3.44971e12 −0.564502
\(695\) 1.47724e13 2.40170
\(696\) 1.32032e13 2.13274
\(697\) 0 0
\(698\) 2.95060e12 0.470501
\(699\) −3.68778e12 −0.584275
\(700\) −3.64568e13 −5.73902
\(701\) 1.96914e12 0.307997 0.153998 0.988071i \(-0.450785\pi\)
0.153998 + 0.988071i \(0.450785\pi\)
\(702\) 2.44944e12 0.380670
\(703\) 7.00790e12 1.08215
\(704\) 2.12234e12 0.325639
\(705\) 2.53950e12 0.387166
\(706\) 2.23269e12 0.338227
\(707\) 8.65751e12 1.30318
\(708\) 1.15845e13 1.73272
\(709\) −3.28723e12 −0.488565 −0.244283 0.969704i \(-0.578552\pi\)
−0.244283 + 0.969704i \(0.578552\pi\)
\(710\) −2.64615e13 −3.90798
\(711\) 1.06848e13 1.56802
\(712\) 1.38781e13 2.02381
\(713\) −5.71933e11 −0.0828785
\(714\) 0 0
\(715\) −7.76864e12 −1.11165
\(716\) −8.83899e12 −1.25688
\(717\) −4.10755e12 −0.580426
\(718\) 6.14445e12 0.862825
\(719\) 1.73463e12 0.242062 0.121031 0.992649i \(-0.461380\pi\)
0.121031 + 0.992649i \(0.461380\pi\)
\(720\) 1.39065e13 1.92851
\(721\) 7.59201e12 1.04628
\(722\) −4.94066e12 −0.676655
\(723\) 1.19239e13 1.62292
\(724\) 2.10243e13 2.84379
\(725\) −9.65255e12 −1.29754
\(726\) 1.28323e13 1.71431
\(727\) −4.39497e12 −0.583514 −0.291757 0.956492i \(-0.594240\pi\)
−0.291757 + 0.956492i \(0.594240\pi\)
\(728\) −3.13374e13 −4.13496
\(729\) −5.63034e12 −0.738347
\(730\) −2.03972e13 −2.65839
\(731\) 0 0
\(732\) −2.56220e13 −3.29848
\(733\) −7.92679e12 −1.01421 −0.507107 0.861883i \(-0.669285\pi\)
−0.507107 + 0.861883i \(0.669285\pi\)
\(734\) −1.06059e13 −1.34869
\(735\) −3.07217e13 −3.88286
\(736\) 8.60025e11 0.108034
\(737\) 2.70850e12 0.338162
\(738\) −1.15813e13 −1.43716
\(739\) 2.29373e12 0.282906 0.141453 0.989945i \(-0.454823\pi\)
0.141453 + 0.989945i \(0.454823\pi\)
\(740\) −3.86051e13 −4.73263
\(741\) 1.12030e13 1.36507
\(742\) −8.66315e12 −1.04920
\(743\) −2.14410e11 −0.0258104 −0.0129052 0.999917i \(-0.504108\pi\)
−0.0129052 + 0.999917i \(0.504108\pi\)
\(744\) 7.35296e12 0.879800
\(745\) −1.14886e13 −1.36636
\(746\) −6.44451e12 −0.761842
\(747\) 2.76105e12 0.324437
\(748\) 0 0
\(749\) 2.59249e13 3.00988
\(750\) −2.17154e13 −2.50606
\(751\) 6.59796e12 0.756885 0.378442 0.925625i \(-0.376460\pi\)
0.378442 + 0.925625i \(0.376460\pi\)
\(752\) −2.06870e12 −0.235895
\(753\) 1.15152e13 1.30526
\(754\) −1.57441e13 −1.77397
\(755\) −3.74953e12 −0.419967
\(756\) −5.34690e12 −0.595325
\(757\) 7.92736e12 0.877399 0.438700 0.898634i \(-0.355439\pi\)
0.438700 + 0.898634i \(0.355439\pi\)
\(758\) 6.30993e12 0.694246
\(759\) 1.71284e12 0.187339
\(760\) −2.30636e13 −2.50765
\(761\) 1.21277e13 1.31084 0.655419 0.755266i \(-0.272492\pi\)
0.655419 + 0.755266i \(0.272492\pi\)
\(762\) 2.15405e13 2.31451
\(763\) −2.82407e12 −0.301658
\(764\) −2.77324e13 −2.94487
\(765\) 0 0
\(766\) 1.68104e13 1.76421
\(767\) −7.27989e12 −0.759532
\(768\) 2.67841e13 2.77813
\(769\) 8.69590e12 0.896697 0.448349 0.893859i \(-0.352012\pi\)
0.448349 + 0.893859i \(0.352012\pi\)
\(770\) 2.49795e13 2.56080
\(771\) −2.40034e12 −0.244640
\(772\) 3.51500e13 3.56162
\(773\) −8.84251e12 −0.890775 −0.445387 0.895338i \(-0.646934\pi\)
−0.445387 + 0.895338i \(0.646934\pi\)
\(774\) −3.18158e12 −0.318646
\(775\) −5.37557e12 −0.535263
\(776\) −1.31173e13 −1.29858
\(777\) −3.17761e13 −3.12756
\(778\) −2.30878e13 −2.25930
\(779\) 7.50374e12 0.730061
\(780\) −6.17153e13 −5.96991
\(781\) 7.64346e12 0.735124
\(782\) 0 0
\(783\) −1.41568e12 −0.134598
\(784\) 2.50263e13 2.36578
\(785\) 2.59062e13 2.43496
\(786\) 3.78288e13 3.53526
\(787\) −1.58211e13 −1.47011 −0.735054 0.678008i \(-0.762843\pi\)
−0.735054 + 0.678008i \(0.762843\pi\)
\(788\) 4.26173e13 3.93747
\(789\) −1.14885e13 −1.05540
\(790\) 5.61754e13 5.13127
\(791\) 2.73427e13 2.48340
\(792\) −1.02821e13 −0.928580
\(793\) 1.61013e13 1.44587
\(794\) 2.55401e13 2.28050
\(795\) −8.99113e12 −0.798293
\(796\) −2.78388e12 −0.245778
\(797\) −7.81310e12 −0.685900 −0.342950 0.939354i \(-0.611426\pi\)
−0.342950 + 0.939354i \(0.611426\pi\)
\(798\) −3.60226e13 −3.14458
\(799\) 0 0
\(800\) 8.08334e12 0.697728
\(801\) 1.05043e13 0.901611
\(802\) −2.29518e13 −1.95899
\(803\) 5.89178e12 0.500065
\(804\) 2.15168e13 1.81604
\(805\) −8.13436e12 −0.682719
\(806\) −8.76800e12 −0.731801
\(807\) −9.15026e12 −0.759456
\(808\) −1.87358e13 −1.54640
\(809\) −1.10974e13 −0.910862 −0.455431 0.890271i \(-0.650515\pi\)
−0.455431 + 0.890271i \(0.650515\pi\)
\(810\) −3.89338e13 −3.17793
\(811\) −2.59323e12 −0.210497 −0.105249 0.994446i \(-0.533564\pi\)
−0.105249 + 0.994446i \(0.533564\pi\)
\(812\) 3.43680e13 2.77429
\(813\) −4.25540e12 −0.341612
\(814\) 1.64257e13 1.31134
\(815\) 1.36978e13 1.08753
\(816\) 0 0
\(817\) 2.06140e12 0.161869
\(818\) −1.24436e13 −0.971755
\(819\) −2.37191e13 −1.84213
\(820\) −4.13366e13 −3.19281
\(821\) −5.84654e12 −0.449112 −0.224556 0.974461i \(-0.572093\pi\)
−0.224556 + 0.974461i \(0.572093\pi\)
\(822\) 4.98810e13 3.81076
\(823\) −2.17086e13 −1.64942 −0.824711 0.565554i \(-0.808662\pi\)
−0.824711 + 0.565554i \(0.808662\pi\)
\(824\) −1.64299e13 −1.24155
\(825\) 1.60989e13 1.20991
\(826\) 2.34080e13 1.74966
\(827\) 2.04178e13 1.51787 0.758935 0.651167i \(-0.225720\pi\)
0.758935 + 0.651167i \(0.225720\pi\)
\(828\) 6.35351e12 0.469761
\(829\) 1.14245e13 0.840119 0.420060 0.907496i \(-0.362009\pi\)
0.420060 + 0.907496i \(0.362009\pi\)
\(830\) 1.45163e13 1.06170
\(831\) −1.84498e13 −1.34211
\(832\) −1.05952e13 −0.766573
\(833\) 0 0
\(834\) −4.99319e13 −3.57380
\(835\) 2.07821e12 0.147945
\(836\) 1.26414e13 0.895089
\(837\) −7.88403e11 −0.0555244
\(838\) −1.12259e13 −0.786362
\(839\) −2.33259e13 −1.62521 −0.812607 0.582813i \(-0.801952\pi\)
−0.812607 + 0.582813i \(0.801952\pi\)
\(840\) 1.04578e14 7.24742
\(841\) −5.40765e12 −0.372758
\(842\) 4.50277e13 3.08727
\(843\) −1.05204e13 −0.717475
\(844\) 1.96416e13 1.33240
\(845\) 1.47104e13 0.992587
\(846\) −4.00797e12 −0.269003
\(847\) 1.76030e13 1.17520
\(848\) 7.32428e12 0.486389
\(849\) −3.75236e13 −2.47868
\(850\) 0 0
\(851\) −5.34888e12 −0.349607
\(852\) 6.07209e13 3.94785
\(853\) −1.94665e12 −0.125897 −0.0629486 0.998017i \(-0.520050\pi\)
−0.0629486 + 0.998017i \(0.520050\pi\)
\(854\) −5.17725e13 −3.33072
\(855\) −1.74567e13 −1.11716
\(856\) −5.61044e13 −3.57162
\(857\) 1.09250e13 0.691842 0.345921 0.938264i \(-0.387567\pi\)
0.345921 + 0.938264i \(0.387567\pi\)
\(858\) 2.62586e13 1.65417
\(859\) 1.59827e13 1.00157 0.500783 0.865573i \(-0.333045\pi\)
0.500783 + 0.865573i \(0.333045\pi\)
\(860\) −1.13559e13 −0.707908
\(861\) −3.40244e13 −2.10997
\(862\) 1.63862e12 0.101087
\(863\) 8.53563e12 0.523826 0.261913 0.965091i \(-0.415647\pi\)
0.261913 + 0.965091i \(0.415647\pi\)
\(864\) 1.18553e12 0.0723773
\(865\) −2.59937e13 −1.57869
\(866\) 3.86646e13 2.33606
\(867\) 0 0
\(868\) 1.91398e13 1.14445
\(869\) −1.62264e13 −0.965234
\(870\) 5.25407e13 3.10928
\(871\) −1.35215e13 −0.796053
\(872\) 6.11159e12 0.357956
\(873\) −9.92843e12 −0.578518
\(874\) −6.06369e12 −0.351508
\(875\) −2.97886e13 −1.71796
\(876\) 4.68053e13 2.68551
\(877\) 1.45232e13 0.829021 0.414511 0.910044i \(-0.363953\pi\)
0.414511 + 0.910044i \(0.363953\pi\)
\(878\) 5.57411e13 3.16555
\(879\) 1.50299e13 0.849192
\(880\) −2.11190e13 −1.18714
\(881\) 2.79317e13 1.56209 0.781044 0.624476i \(-0.214688\pi\)
0.781044 + 0.624476i \(0.214688\pi\)
\(882\) 4.84866e13 2.69782
\(883\) −1.95980e13 −1.08490 −0.542450 0.840088i \(-0.682503\pi\)
−0.542450 + 0.840088i \(0.682503\pi\)
\(884\) 0 0
\(885\) 2.42942e13 1.33125
\(886\) 1.14124e13 0.622196
\(887\) −1.87122e13 −1.01501 −0.507504 0.861650i \(-0.669432\pi\)
−0.507504 + 0.861650i \(0.669432\pi\)
\(888\) 6.87670e13 3.71126
\(889\) 2.95487e13 1.58665
\(890\) 5.52264e13 2.95047
\(891\) 1.12461e13 0.597794
\(892\) −1.53861e13 −0.813742
\(893\) 2.59683e12 0.136651
\(894\) 3.88324e13 2.03318
\(895\) −1.85365e13 −0.965658
\(896\) 4.76815e13 2.47152
\(897\) −8.55088e12 −0.441006
\(898\) 1.70277e13 0.873799
\(899\) 5.06757e12 0.258751
\(900\) 5.97164e13 3.03391
\(901\) 0 0
\(902\) 1.75879e13 0.884676
\(903\) −9.34707e12 −0.467822
\(904\) −5.91726e13 −2.94688
\(905\) 4.40905e13 2.18487
\(906\) 1.26737e13 0.624923
\(907\) 1.04166e12 0.0511085 0.0255542 0.999673i \(-0.491865\pi\)
0.0255542 + 0.999673i \(0.491865\pi\)
\(908\) −7.98848e13 −3.90012
\(909\) −1.41810e13 −0.688922
\(910\) −1.24704e14 −6.02827
\(911\) 2.23220e13 1.07374 0.536871 0.843665i \(-0.319606\pi\)
0.536871 + 0.843665i \(0.319606\pi\)
\(912\) 3.04554e13 1.45777
\(913\) −4.19305e12 −0.199715
\(914\) 3.66895e13 1.73894
\(915\) −5.37326e13 −2.53421
\(916\) 1.75791e13 0.825025
\(917\) 5.18925e13 2.42350
\(918\) 0 0
\(919\) 2.33385e13 1.07933 0.539665 0.841880i \(-0.318551\pi\)
0.539665 + 0.841880i \(0.318551\pi\)
\(920\) 1.76036e13 0.810135
\(921\) 3.65547e13 1.67407
\(922\) 5.30152e13 2.41608
\(923\) −3.81579e13 −1.73052
\(924\) −5.73202e13 −2.58692
\(925\) −5.02739e13 −2.25790
\(926\) −9.42764e12 −0.421360
\(927\) −1.24357e13 −0.553112
\(928\) −7.62020e12 −0.337288
\(929\) −3.89397e13 −1.71523 −0.857614 0.514293i \(-0.828054\pi\)
−0.857614 + 0.514293i \(0.828054\pi\)
\(930\) 2.92603e13 1.28264
\(931\) −3.14153e13 −1.37046
\(932\) 2.07739e13 0.901876
\(933\) −1.60122e13 −0.691807
\(934\) 1.18732e13 0.510514
\(935\) 0 0
\(936\) 5.13307e13 2.18593
\(937\) −4.23162e13 −1.79340 −0.896702 0.442634i \(-0.854044\pi\)
−0.896702 + 0.442634i \(0.854044\pi\)
\(938\) 4.34774e13 1.83379
\(939\) −3.87357e13 −1.62598
\(940\) −1.43054e13 −0.597621
\(941\) −4.34990e13 −1.80853 −0.904266 0.426970i \(-0.859581\pi\)
−0.904266 + 0.426970i \(0.859581\pi\)
\(942\) −8.75652e13 −3.62328
\(943\) −5.72734e12 −0.235858
\(944\) −1.97904e13 −0.811110
\(945\) −1.12131e13 −0.457386
\(946\) 4.83168e12 0.196150
\(947\) −3.51130e13 −1.41871 −0.709354 0.704853i \(-0.751013\pi\)
−0.709354 + 0.704853i \(0.751013\pi\)
\(948\) −1.28905e14 −5.18361
\(949\) −2.94131e13 −1.17718
\(950\) −5.69924e13 −2.27018
\(951\) −1.97322e12 −0.0782281
\(952\) 0 0
\(953\) 5.36351e12 0.210635 0.105318 0.994439i \(-0.466414\pi\)
0.105318 + 0.994439i \(0.466414\pi\)
\(954\) 1.41903e13 0.554655
\(955\) −5.81582e13 −2.26254
\(956\) 2.31386e13 0.895934
\(957\) −1.51765e13 −0.584881
\(958\) 1.54077e13 0.591008
\(959\) 6.84254e13 2.61236
\(960\) 3.53579e13 1.34359
\(961\) −2.36175e13 −0.893260
\(962\) −8.20009e13 −3.08696
\(963\) −4.24651e13 −1.59116
\(964\) −6.71695e13 −2.50510
\(965\) 7.37140e13 2.73638
\(966\) 2.74948e13 1.01590
\(967\) 3.98866e13 1.46693 0.733463 0.679729i \(-0.237903\pi\)
0.733463 + 0.679729i \(0.237903\pi\)
\(968\) −3.80948e13 −1.39453
\(969\) 0 0
\(970\) −5.21989e13 −1.89317
\(971\) −2.58744e13 −0.934079 −0.467039 0.884237i \(-0.654679\pi\)
−0.467039 + 0.884237i \(0.654679\pi\)
\(972\) 7.93418e13 2.85104
\(973\) −6.84952e13 −2.44992
\(974\) 1.49580e13 0.532546
\(975\) −8.03694e13 −2.84820
\(976\) 4.37712e13 1.54406
\(977\) −4.14893e13 −1.45684 −0.728418 0.685133i \(-0.759744\pi\)
−0.728418 + 0.685133i \(0.759744\pi\)
\(978\) −4.62997e13 −1.61828
\(979\) −1.59522e13 −0.555008
\(980\) 1.73061e14 5.99351
\(981\) 4.62583e12 0.159470
\(982\) −8.96151e13 −3.07524
\(983\) −2.21812e13 −0.757695 −0.378847 0.925459i \(-0.623679\pi\)
−0.378847 + 0.925459i \(0.623679\pi\)
\(984\) 7.36326e13 2.50376
\(985\) 8.93737e13 3.02515
\(986\) 0 0
\(987\) −1.17749e13 −0.394939
\(988\) −6.31087e13 −2.10709
\(989\) −1.57339e12 −0.0522943
\(990\) −4.09166e13 −1.35376
\(991\) −1.15492e13 −0.380382 −0.190191 0.981747i \(-0.560911\pi\)
−0.190191 + 0.981747i \(0.560911\pi\)
\(992\) −4.24374e12 −0.139138
\(993\) −8.07709e12 −0.263623
\(994\) 1.22694e14 3.98644
\(995\) −5.83816e12 −0.188830
\(996\) −3.33102e13 −1.07253
\(997\) −2.07044e13 −0.663643 −0.331821 0.943342i \(-0.607663\pi\)
−0.331821 + 0.943342i \(0.607663\pi\)
\(998\) 8.22293e13 2.62385
\(999\) −7.37337e12 −0.234218
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))

Twists

       By twisting character
Char Parity Ord Type Twist Min Dim
1.1 even 1 trivial 289.10.a.g.1.34 36
17.16 even 2 289.10.a.h.1.34 yes 36
    
        By twisted newform
Twist Min Dim Char Parity Ord Type
289.10.a.g.1.34 36 1.1 even 1 trivial
289.10.a.h.1.34 yes 36 17.16 even 2